Radial Orbit Error Research Articles

Crossover adjustment of ICESat-2 satellite altimetry for the Arctic region

The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) mission, operated by NASA, was launched in September 2018. The mission aims to obtain height measurements that create a global portrait of Earth’s radial dimension, gathering data to monitor changes of terrain including glaciers, sea ice, forests and more. It is important to understand the error budget of the observations, one component of which is radial orbit error. Apart from the altimetric ranging errors, radial orbit errors directly influence the accuracy of the measurement of sea surface height (SSH). These errors can be assessed by analyzing the difference of SSHs at ground track intersections, so-called crossover differences (XO differences). An effective approach is to model the orbit error by minimizing the residual XO difference by the least-squares method. XO differences are assumed to be caused by the difference of radial orbit errors between ascending and descending arcs, the sea surface variation, mispointing, and measurement errors. Since the sea surface variation in a short time interval and measurement errors can be considered as random variable, these residuals can be reduced by the method of XO adjustment. In our study, the RMS XO differences of ICESat-2 is significantly reduced from 17.2 cm to 8.7 cm in the Arctic region.

Advancing the Solar Radiation Pressure Model for BeiDou-3 IGSO Satellites

In the absence of detailed surface information, empirical solar radiation pressure (SRP) models, such as the five-parameter Empirical CODE Orbit Model (ECOM1) and its extended version-ECOM2, are widely used for modeling SRP forces acting on GNSS satellites. This study shows that the orbits of BeiDou-3 Inclined Geosynchronous Orbit satellites (IGSOs) determined with the ECOM1 model suffer from systematic once-per-revolution radial orbit errors, which can be partly reduced by the ECOM2 model. To eliminate such orbit errors, the BeiDou-3 IGSO optical coefficients are solved by using an adjustable box-wing (ABW) model and then introduced into an a priori box-wing SRP model to enhance the ECOM1 model (ECOM1 + BW). In the ABW solution, in addition to satellite body and solar panels, the contributions of the communication payloads installed on BeiDou-3 IGSO ±X panels on the SRP are also considered, which markedly improves the stability of the optical coefficient estimates. The efficiency of the developed a priori box-wing model is demonstrated through eliminated once-per-revolution radial orbit errors and decreased day boundary discontinuities. However, the orbit solutions still show significant degradations during eclipse seasons. The results of the first yaw-attitude analysis for eclipsing BeiDou-3 IGSOs show that their yaw behaviors are the same as those of BeiDou-3 CAST (China Academy of Space Technology) MEOs (Medium Earth Orbit satellites), and have been well considered in the study. This rules out the possibility that attitude errors are the potential reason for the orbit deterioration. By introducing a once-per-revolution sine term in the Sun direction (Ds term) and keeping Ds active during the Earth’s shadow transitions to the ECOM1 + BW model, the orbit performance inside the eclipse seasons is significantly improved and can be comparable to that outside the eclipse seasons.

Sentinel-6A precise orbit determination using a combined GPS/Galileo receiver

The Sentinel-6 (or Jason-CS) altimetry mission provides a long-term extension of the Topex and Jason-1/2/3 missions for ocean surface topography monitoring. Analysis of altimeter data relies on highly-accurate knowledge of the orbital position and requires radial RMS orbit errors of less than 1.5 cm. For precise orbit determination (POD), the Sentinel-6A spacecraft is equipped with a dual-constellation GNSS receiver. We present the results of Sentinel-6A POD solutions for the first 6 months since launch and demonstrate a 1-cm consistency of ambiguity-fixed GPS-only and Galileo-only solutions with the dual-constellation product. A similar performance (1.3 cm 3D RMS) is achieved in the comparison of kinematic and reduced-dynamic orbits. While Galileo measurements exhibit 30–50% smaller RMS errors than those of GPS, the POD benefits most from the availability of an increased number of satellites in the combined dual-frequency solution. Considering obvious uncertainties in the pre-mission calibration of the GNSS receiver antenna, an independent inflight calibration of the phase centers for GPS and Galileo signal frequencies is required. As such, Galileo observations cannot provide independent scale information and the estimated orbital height is ultimately driven by the employed forces models and knowledge of the center-of-mass location within the spacecraft. Using satellite laser ranging (SLR) from selected high-performance stations, a better than 1 cm RMS consistency of SLR normal points with the GNSS-based orbits is obtained, which further improves to 6 mm RMS when adjusting site-specific corrections to station positions and ranging biases. For the radial orbit component, a bias of less than 1 mm is found from the SLR analysis relative to the mean height of 13 high-performance SLR stations. Overall, the reduced-dynamic orbit determination based on GPS and Galileo tracking is considered to readily meet the altimetry-related Sentinel-6 mission needs for RMS height errors of less than 1.5 cm.

Preliminary assessment of BeiDou Navigation Satellite System satellite orbit determination accuracy and positioning accuracy

Orbit determination accuracy and positioning accuracy are two key indexes to assess the performance of navigation system. With frontal positioning methods put forward, the effect of orbit determination accuracy on positioning accuracy is decreasing. In this paper, three main positioning methods provided by BDS is introduced, and the influence of BDS orbit determination accuracy on the results of single point positioning, differential positioning and precise point positioning is respectively deduced. After that, data from two receivers set at Beijing and Chengdu is analysed to evaluate orbit determination accuracy and positioning accuracy. Apart from several extreme values, BDS satellites radial orbit errors are within 1.5m, tangential orbit errors are within 2m and normal orbit errors are less than 5m. Accuracy of single point positioning differential positioning and precise point positioning is 1.9m 1.2m and 0.3m, respectively. Effect of orbit determination accuracy on single point positioning is significant. On the other hand, orbit determination accuracy has less effect on differential positioning accuracy and precise point positioning.

Analysis of signal-in-space ranging error of GNSS navigation message

The signal-in-space ranging error (SISRE) is a major factor that affects the accuracy of positioning and timing. It describes the projection of the satellite-broadcast ephemeris error and clock difference error in the average direction from satellites to stations. In this study, the size and characteristics of the broadcast ephemeris user range error (URE), clock difference error, and SISRE are evaluated with respect to GPS, Galileo, and BDS-3. The results indicate that the SISREs of Galileo, GPS, and BDS-3 are 0.14, 0.49, and 0.35 m, respectively, the broadcast ephemeris UREs of Galileo, GPS, and BDS-3 are 0.14, 0.27, and 0.09 m, respectively, and the clock difference errors of Galileo, GPS, and BDS-3 are 0.14, 0.41, and 0.35 m, respectively. In case of Galileo, the radial orbit error and the clock difference error exhibit strong correlation. Both these errors cancel each other, and the SISRE associated with Galileo can be effectively reduced. Further, obvious differences can be observed with respect to the clock difference error and SISRE in case of different types of GPS satellites. The clock difference error and SISRE of GPS will gradually decrease with the upgradation of satellites. The SISRE of BDS-3 exhibits different characteristics when compared with those exhibited by the SISREs of GPS and Galileo. First, the radial error of BDS-3 is less correlated with the clock difference error, which exhibits poor self-consistency. Second, the BDS-3 satellite-broadcast ephemeris URE is small, whereas the clock difference error is large. Furthermore, the broadcast ephemeris URE associated with BDS-3 is lower than those associated with Galileo and GPS. However, the contribution of the clock difference error associated with BDS-3 to SISRE is considerably greater than those of the clock difference errors associated with GPS and Galileo to SISRE. In this study, the sizes and characteristics of the SISRE of BDS-3, Galileo, and GPS are compared, indicating that signal-in-space accuracy of BDS-3 can be improved by reducing the clock difference error.

Orbit and clock analysis of BDS-3 satellites using inter-satellite link observations

China is currently focusing on the establishment of its BDS-3 system, and a BDS-3 constellation with 18 satellites in medium Earth orbit (MEO) and one satellite in geostationary Earth orbit (GEO) has been able to provide preliminary global services since the end of 2018. These BDS-3 satellites feature the inter-satellite link (ISL) and new high-quality onboard clocks. In this study, we present the analysis of BDS-3 orbits and clocks determined by Ka-band ISL measurements from 18 MEO satellites and one GEO satellite. The ISL data of 43 days from 1 January to 12 February 2019 are used. The BDS-3 ISL measurement is described by a dual one-way ranging model. After converting bidirectional observations to the same epoch, Ka-band clock-free and geometry-free observables are obtained by the addition and subtraction of dual one-way observations, respectively. One anchor station with Ka-band bidirectional observations is introduced into the orbit determination to provide the orientation constraints. Using Ka-band clock-free observables, BDS-3 satellite orbits are determined. The ISL hardware delays are estimated together with orbits, and the resulting hardware delay estimates are quite stable with STD of about 0.03 ns. The Ka-band orbits are evaluated by orbit overlap differences, comparison with L-band precise orbits, and satellite laser ranging validation. The results indicate that the radial orbit errors are on the 2–4 cm level for MEO satellites and 8–10 cm for the GEO satellite. In addition, we investigate the ground anchoring capability by adding one anchor station and reducing the amount of data of the anchor station. Using Ka-band geometry-free observables, BDS-3 satellite clocks are estimated and the RMS of post-fit ISL residuals is about 5 cm. The Ka-band clock offsets are analyzed and compared with L-band precise clocks. Independent of orbit errors, the Allan deviation of Ka-band clocks for averaging interval longer than 5000 s is superior to that of L-band clocks. Furthermore, a pronounced bump, which appears in the Allan deviation of L-band clocks, almost vanishes in Ka-band clocks. Finally, the periodic variations are detected for L-band and Ka-band clocks.

A shadow function model based on perspective projection and atmospheric effect for satellites in eclipse

Accurate Solar Radiation Pressure (SRP) modelling is critical for correctly describing the dynamics of satellites. A shadow function is a unitless quantity varying between 0 and 1 to scale the solar radiation flux at a satellite’s location during eclipses. Errors in modelling shadow function lead to inaccuracy in SRP that degrades the orbit quality. Shadow function modelling requires solutions to a geometrical problem (Earth’s oblateness) and a physical problem (atmospheric effects). This study presents a new shadow function model (PPM_atm) which uses a perspective projection based approach to solve the geometrical problem rigorously and a linear function to describe the reduction of solar radiation flux due to atmospheric effects. GRACE (Gravity Recovery And Climate Experiment) satellites carry accelerometers that record variations of non-conservative forces, which reveal the variations of shadow function during eclipses. In this study, the PPM_atm is validated using accelerometer observations of the GRACE-A satellite. Test results show that the PPM_atm is closer to the variations in accelerometer observations than the widely used SECM (Spherical Earth Conical Model). Taking the accelerometer observations derived shadow function as the “truth”, the relative error in PPM_atm is −0.79% while the SECM 11.07%. The influence of the PPM_atm is also shown in orbit prediction for Galileo satellites. Compared with the SECM, the PPM_atm can reduce the radial orbit error RMS by 5.6 cm over a 7-day prediction. The impacts of the errors in shadow function modelling on the orbit remain to be systematic and should be mitigated in long-term orbit prediction.

Impact of ITRS 2014 realizations on altimeter satellite precise orbit determination

This paper evaluates orbit accuracy and systematic error for altimeter satellite precise orbit determination on TOPEX, Jason-1, Jason-2 and Jason-3 by comparing the use of four SLR/DORIS station complements from the International Terrestrial Reference System (ITRS) 2014 realizations with those based on ITRF2008. The new Terrestrial Reference Frame 2014 (TRF2014) station complements include ITRS realizations from the Institut National de l’Information Géographique et Forestière (IGN) ITRF2014, the Jet Propulsion Laboratory (JPL) JTRF2014, the Deutsche Geodätisches Forschungsinstitut (DGFI) DTRF2014, and the DORIS extension to ITRF2014 for Precise Orbit Determination, DPOD2014. The largest source of error stems from ITRF2008 station position extrapolation past the 2009 solution end time. The TRF2014 SLR/DORIS complement impact on the ITRF2008 orbit is only 1–2mm RMS radial difference between 1992–2009, and increases after 2009, up to 5mm RMS radial difference in 2016. Residual analysis shows that station position extrapolation error past the solution span becomes evident even after two years, and will contribute to about 3–4mm radial orbit error after seven years. Crossover data show the DTRF2014 orbits are the most accurate for the TOPEX and Jason-2 test periods, and the JTRF2014 orbits for the Jason-1 period. However for the 2016 Jason-3 test period only the DPOD2014-based orbits show a strong and statistically significant margin of improvement. The positive results with DTRF2014 suggest the new approach to correct station positions or normal equations for non-tidal loading before combination is beneficial. We did not find any compelling POD advantage in using non-linear over linear station velocity models in our SLR & DORIS orbit tests on the Jason satellites. The JTRF2014 proof-of-concept ITRS realization demonstrates the need for improved SLR+DORIS orbit centering when compared to the Ries (2013) CM annual model. Orbit centering error is seen asan annual radial signal of 0.4mm amplitude with the CM model. The unmodeled CM signals show roughly a 1.8mm peak-to-peak annual variation in the orbit radial component. We find the TRF network stability pertinent to POD can be defined only by examination of the orbit-specific tracking network time series. Drift stability between the ITRF2008 and the other TRF2014-based orbits is very high, the relative mean radial drift error over water is no larger than 0.04mm/year over 1993–2015. Analyses also show TRF induced orbit error meets current altimeter rate accuracy goals for global and regional sea level estimation.

Enhanced solar radiation pressure modeling for Galileo satellites

This paper introduces a new approach for modeling solar radiation pressure (SRP) effects on Global Navigation Satellite Systems (GNSSs). It focuses on the Galileo In-Orbit Validation (IOV) satellites, for which obvious SRP modeling deficits can be identified in presently available precise orbit products. To overcome these problems, the estimation of empirical accelerations in the Sun direction (D), solar panel axis (Y) and the orthogonal (B) axis is complemented by an a priori model accounting for the contribution of the rectangular spacecraft body. Other than the GPS satellites, which comprise an almost cubic body, the Galileo IOV satellites exhibit a notably rectangular shape with a ratio of about 2:1 for the main body axes. Use of the a priori box model allows to properly model the varying cross section exposed to the Sun during yaw-steering attitude mode and helps to remove systematic once-per-revolution orbit errors that have so far affected the Galileo orbit determination. Parameters of a simple a priori cuboid model suitable for the IOV satellites are established from the analysis of a long-term set of GNSS observations collected with the global network of the Multi-GNSS Experiment of the International GNSS Service. The model is finally demonstrated to reduce the peak magnitude of radial orbit errors from presently 20 cm down to 5 cm outside eclipse phases.

Galileo orbit and clock quality of the IGS Multi-GNSS Experiment

The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) aims at the data collection and analysis of all available satellite navigation systems. In particular the new global and regional satellite navigation systems are of interest, i.e., the European Galileo, the Chinese BeiDou, the Japanese QZSS as well as satellite based augmentation systems. This article analyzes the orbit and clock quality of the Galileo products of four MGEX analysis centers for a common time period of 20weeks. Orbit comparisons of the individual analysis centers have a consistency at the 5–30cm level. Day boundary discontinuities range from 4 to 28cm whereas 2-day orbit fit RMS values vary between 1 and 7cm. The accuracy evaluated by satellite laser ranging residuals is on the one decimeter level with a systematic bias of about −5cm for all analysis centers. In addition, systematic errors on the decimeter level related to solar radiation pressure mismodeling are present in all orbit products. Due to the correlation of radial orbit errors with the clock parameters, these errors are also visible as a bump in the Allan deviation of the Galileo satellite clocks at the orbital frequency.

Precise orbit determination using the batch filter based on particle filtering with genetic resampling approach

In this study, genetic resampling (GRS) approach is utilized for precise orbit determination (POD) using the batch filter based on particle filtering (PF). Two genetic operations, which are arithmetic crossover and residual mutation, are used for GRS of the batch filter based on PF (PF batch filter). For POD, Laser-ranging Precise Orbit Determination System (LPODS) and satellite laser ranging (SLR) observations of the CHAMP satellite are used. Monte Carlo trials for POD are performed by one hundred times. The characteristics of the POD results by PF batch filter with GRS are compared with those of a PF batch filter with minimum residual resampling (MRRS). The post-fit residual, 3D error by external orbit comparison, and POD repeatability are analyzed for orbit quality assessments. The POD results are externally checked by NASA JPL’s orbits using totally different software, measurements, and techniques. For post-fit residuals and 3D errors, both MRRS and GRS give accurate estimation results whose mean root mean square (RMS) values are at a level of 5cm and 10–13cm, respectively. The mean radial orbit errors of both methods are at a level of 5cm. For POD repeatability represented as the standard deviations of post-fit residuals and 3D errors by repetitive PODs, however, GRS yields 25% and 13% more robust estimation results than MRRS for post-fit residual and 3D error, respectively. This study shows that PF batch filter with GRS approach using genetic operations is superior to PF batch filter with MRRS in terms of robustness in POD with SLR observations.

Satellite-station time synchronization information based real-time orbit error monitoring and correction of navigation satellite in Beidou System

Satellite-station two-way time comparison is a typical design in Beidou System (BDS) which is significantly different from other satellite navigation systems. As a type of two-way time comparison method, BDS time synchronization is hardly influenced by satellite orbit error, atmosphere delay, tracking station coordinate error and measurement model error. Meanwhile, single-way time comparison can be realized through the method of Multi-satellite Precision Orbit Determination (MPOD) with pseudo-range and carrier phase of monitor receiver. It is proved in the constellation of 3GEO/2IGSO that the radial orbit error can be reflected in the difference between two-way time comparison and single-way time comparison, and that may lead to a substitute for orbit evaluation by SLR. In this article, the relation between orbit error and difference of two-way and single-way time comparison is illustrated based on the whole constellation of BDS. Considering the all-weather and real-time operation mode of two-way time comparison, the orbit error could be quantifiably monitored in a real-time mode through comparing two-way and single-way time synchronization. In addition, the orbit error can be predicted and corrected in a short time based on its periodic characteristic. It is described in the experiments of GEO and IGSO that the prediction accuracy of space signal can be obviously improved when the prediction orbit error is sent to the users through navigation message, and then the UERE including terminal error can be reduced from 0.1 m to 0.4 m while the average accuracy can be improved more than 27%. Though it is still hard to make accuracy improvement for Precision Orbit Determination (POD) and orbit prediction because of the confined tracking net and the difficulties in dynamic model optimization, in this paper, a practical method for orbit accuracy improvement is proposed based on two-way time comparison which can result in the reflection of orbit error.

Precise orbit determination for Jason-1 satellite using on-board GPS data with cm-level accuracy

The joint US/French Jason-1 satellite altimeter mission, launched from the Vandenberg Air Force Base on December 7, 2001, continues the time series of centimeter-level ocean topography observations as the follow-on to the highly successful T/P radar altimeter satellite. Orbit error especially the radial orbit error is a major component in the overall budget of all altimeter satellite missions, in order to continue the T/P standard of observations. Jason-1 has a radial orbit error budget requirement of 2.5 cm. In this work, two cycles (December 19, 2002 to January 7, 2003) of the Jason-1 on-board GPS data were processed using the zero-difference (ZD) dynamic precise orbit determination (POD) technique. The resulting Jason-1 orbit accuracy was assessed by comparison with the precise orbit ephemeris (POE) produced by JPL, orbit overlaps and SLR residuals. These evaluations indicate that the RMS radial accuracy is in the range of 1–2 cm.

Lunar satellite orbit determination analysis and quality assessment from Lunar Prospector tracking data and SELENE simulations

Low lunar satellite orbit accuracy is assessed by means of the analysis of tracking data residuals, orbit overlap statistics and covariance propagation. A full-scale determination of a degree and order 75 spherical harmonics lunar gravity field model from 3 months of Lunar Prospector tracking data shows the influence of processing strategies for gravity field modelling. Despite large differences in gravity anomalies over the far side between this model and a comparable existing model, both models show similar results in terms of orbit performance. Analysis of residuals and overlap statistics using the LP150Q gravity field model shows the Doppler data fit to be at the level of a few mm/s. Three-dimensional orbit consistency is found to be at the level of 50–300 m, for polar orbits with altitudes ranging from 30 to 100 km. Covariance analysis shows that the expected radial orbit error as computed from the covariance of an anticipated gravity field model using SELENE data will be less than 1 m. Current gravity field models are shown to be tuned towards the polar orbit, while having expected orbit errors of several orders of magnitude larger for other inclinations, especially in the mid-range, from 40° to 80°.

A spectral optimally interpolated mean sea surface from satellite radar altimetry

A technique is presented for the development of a high-precision and high-resolution mean sea surface model utilising radar altimetric sea surface heights extracted from the geodetic phase of the European Space Agency (ESA) ERS-1 mission. The methodology uses a cubic-spline fit of dual ERS-1 and TOPEX crossovers for the minimisation of radial orbit error. Fourier domain processing techniques are used for spectral optimal interpolation of the mean sea surface in order to reduce residual errors within the initial model. The EGM96 gravity field and sea surface topography models are used as reference fields as part of the determination of spectral components required for the optimal interpolation algorithm. A comparison between the final model and 10 cycles of TOPEX sea surface heights shows differences of between 12.3 and 13.8 cm root mean square (RMS). An un-optimally interpolated surface comparison with TOPEX data gave differences of between 15.7 and 16.2 cm RMS. The methodology results in an approximately 10-cm improvement in accuracy. Further improvement will be attained with the inclusion of stacked altimetry from both current and future missions.

A comparison of ocean topography derived from the Shuttle Laser Altimeter-01 and TOPEX/POSEIDON

To assess the utility of laser altimetry for studies in dynamical oceanography, the authors present a comparison of the Shuttle Laser Altimeter (SLA)-01 and the TOPEX/POSEIDON (T/P) radar altimeter on global and regional scales. They compare all /spl sim/1.1 million SLA-01 range measurements over the oceans to the CSRMSS95 gridded mean sea surface model and find the overall root mean square (RMS) difference to be 2.33 m. The misfit was improved significantly by removing the mean and trend from individual SLA-01 profiles, often resulting in RMS differences less than 1 m. They also show that in regions where sea surface height varies dramatically over relatively short horizontal scales such as across major subduction zones, SLA-01 as capable of resolving rapid changes in sea surface height. Finally, they examine a number of coastal zones and illustrate SLA-01's ability to track continuously across the land-sea interface, even in regions of dramatic coastal topography. The dominant sources of radial error in the SLA-01 data are time-interval unit (TIU) error (/spl plusmn/0.75 m) and radial orbit error (1 m RMS). Therefore, limitations of the SLA-01 data set are caused primarily by system constraints as opposed to instrumentation error. Their results indicate that future laser altimeters will provide valuable information regarding ocean topography. In particular, laser altimetry data can be used to supplement orbiting microwave ranging systems in coastal areas where such sensors are incapable of maintaining lock across the continent-ocean transition.

Ice flow physical processes derived from the ERS-1 high-resolution map of the Antarctica and Greenland ice sheets

Accepted 1999 July 7. Received 1999 June 7; in original form 1998 June 24 SUMMARY The ERS-1 satellite, launched in 1991, has provided altimetric observations of the Greenland Ice Sheet and 80 per cent of the Antarctica Ice Sheet north of 82°S. It was placed in a geodetic (168-day repeat) orbit between April 1994 and March 1995, yielding a 1.5 km across-track spacing at latitude 70° with a higher along-track sampling of 350 m. We have analysed the waveform altimetric data from this period to compute maps with a 1/30° grid size. Data processing consists of correcting for environmental factors and editing and retracking the waveforms. A further step consists of reducing the radial orbit error through crossover analysis and correcting the slope error to second order. The high-resolution topography of both ice sheets reveals numerous details. A kilometre-scale surface roughness running at 45° from the flow direction is the dominant topographic characteristic of both continents. Antarctica also exhibits many scars due to local flow anomalies. Several physical processes can be identified: abrupt transitions from deformation to sliding and vice versa, and impressive strike-slip phenomena, inducing en echelon folds.

On the analysis of repeated geodetic experiments

In the linear estimation problem associated with an experiment that is exactly repeated a number of times, the estimation parameters may naturally be partitioned into two groups, those that are common to all repetitions, and those that are particular to each repeat experiment. We derive least-squares solutions that minimise in norm either group of parameters, as also the trace of the corresponding covariance matrix. These solutions are applied to the station adjustment of triangulation surveying, and to the estimation problem of satellite radar altimetry: to estimate simultaneously mean sea surface heights and residual radial orbit errors, while minimising the norm of either group of parameters. This altimetry problem is considered in the cases of collinear, local crossover and global crossover data.

Lunar albedo force modeling and its effect on low lunar orbit and gravity field determination

A force model for the lunar albedo effect on low lunar orbiters is developed on the basis of Clementine imagery and absolute albedo measurements. The model, named the Delft Lunar Albedo Model 1 (DLAM-1), is a 15 × 15 spherical harmonics expansion, and is intended for improved force modeling for low satellite orbits as well as to minimise aliasing of non-gravitational force model defects in future lunar gravity solutions. The development of the model from the available lunar albedo data sources is described, followed by a discussion on its calibration using absolute albedo measurements and its correlation with main selenological features. DLAM-1 is next applied in low lunar orbit determination, and results for orbits typical of lunar mapping missions are presented. Finally, the effect of lunar albedo on future gravity solutions is analysed with particular emphasis on gravity mapping from global data sets, i.e. satellite-to-satellite tracking, which is expected to be a core experiment of coming lunar missions. It is shown that albedo-induced orbit perturbations have a magnitude and frequency signature which are non-negligible for precise orbit and gravity modeling. Radial orbit errors for low orbits are in the order of 1–2 m for one week arcs.

Accuracy assessment and refinement of the JGM-2 and JGM-3 gravity fields for radial positioning of ERS-1

ERS-1 radial positioning using the JGM-2 and JGM-3 gravity fields is assessed by analysing dual crossovers with TOPEX/Poseidon, neither field containing ERS-1 data. This method allows a more complete recovery of ERS-1 radial orbit error, specifically of the previously unattainable mean geographical error. The global analysis shows that the theoretical error derived from the JGM-2 covariance matrix is realistic and that JGM-3 represents a slight improvement, at least at the inclination of ERS-1. A latitudinal-based study in the southern ocean indicates possible weaknesses in both fields, notably for low and resonant geopotential orders m. A refinement of JGM-2, RGM-2, is undertaken through inclusion of ERS-1 and STELLA laser tracking and ERS-1 altimetry, reducing several of its deficiencies.